The misuse of significance tests in econometrics is part of the larger problem of formal criteria that have been imposed and must be respected if one wishes to publish, at least in a mainstream journal. For example, in macroeconomics one is expected to base ones model on the assumption of a rational, utility maximizing representative agent, even though there exists a vast literature that demonstrates that the representative agent cannot be justified by any plausible set of assumptions. The requirements change as research programs change, but they never have a scientific justification. In the post-WWII era for example, it was thought that a macro-econometric model, to be of any use, must have hundreds, perhaps more than one thousand equations.

I believe that the slave like adherence to absurd formal criteria is a consequence of the recruitment practices in economics over essentially the past half century. There was a vast expansion in the number of professional economist, while the principal criterion of admission was some degree of mathematical competence. A specific interest in economics was not required. Many who became professors of economics must have chosen this career in the same way as one chooses to become a dentist or a lawyer. Their education consisted essentially of learning to solve the problems that they were presented with, without much thought as to their relevance. This is how they continued to work as professional economists. If they had learned how to formulate and estimate, say a rational expectations model, including significance tests, then that is what they did and were expected to do in order to be able to publish in mainstream journals.

I think the problem viewed this way is rather simple, but unfortunately unsolvable, at least over the foreseeable future.